Exciting space-time surface plasmon polaritons by irradiating a nanoslit structure.

Space-time (ST) wave packets are propagation-invariant pulsed optical beams that travel freely in dielectrics at a tunable group velocity without diffraction or dispersion. Because ST wave packets maintain these characteristics even when only one transverse dimension is considered, they can realize surface-bound waves (e.g.

Universal angular-dispersion synthesizer.

We uncover a surprising gap in optics with regards to angular dispersion (AD). A systematic examination of pulsed optical field configurations classified according to their three lowest dispersion orders resulting from AD (the axial phase velocity, group velocity, and group-velocity dispersion) reveals that the majority of possible classes of fields have eluded optics thus far. This gap is due in part to the limited technical reach of the standard components that provide AD such as gratings and prisms, but due in part also to misconceptions regarding the set of physically admissible field configurations that can be accessed via AD.

Compact dual-band spectral analysis via multiplexed rotated chirped volume Bragg gratings.

Chirped Bragg volume gratings (CBGs) offer a useful alternative for spectral analysis, but increasing the bandwidth necessitates increasing the device area. In contrast, recently developed rotated CBGs (r-CBGs), in which the Bragg structure is rotated by 45° with respect to the device facets, require increasing only the device length to extend the bandwidth, in addition to the convenience of resolving the spectrum at normal incidence. Here, we multiplex r-CBGs in the same device to enable spectral analysis in two independent spectral windows without increasing the system volume.

Theory of space-time supermodes in planar multimode waveguides.

When an optical pulse is focused into a multimode waveguide or fiber, the energy is divided among the available guided modes. Consequently, the initially localized intensity spreads transversely, the spatial profile undergoes rapid variations with axial propagation, and the pulse disperses temporally. Space-time (ST) supermodes are pulsed guided field configurations that propagate invariantly in multimode waveguides by assigning each mode to a prescribed wavelength.

Ultra-compact synthesis of space-time wave packets.

Space-time wave packets (STWPs) are pulsed fields in which a strictly prescribed association between the spatial and temporal frequencies yields surprising and useful behavior. However, STWPs to date have been synthesized using bulky free-space optical systems that require precise alignment. We describe a compact system that makes use of a novel optical component: a chirped volume Bragg grating that is rotated by 45° with respect to the plane-parallel device facets.

Rotated chirped volume Bragg gratings for compact spectral analysis.

We introduce a new, to the best of our knowledge, optical component-a rotated chirped volume Bragg grating (r-CBG)-that spatially resolves the spectrum of a normally incident light beam in a compact footprint and without the need for subsequent free-space propagation or collimation. Unlike conventional chirped volume Bragg gratings in which both the length and width of the device must be increased to increase the bandwidth, by rotating the Bragg structure we sever the link between the length and width of a r-CBG, leading to a significantly reduced device footprint for the same bandwidth. We fabricate and characterize such a device in multiple spectral windows, we study its spectral resolution, and confirm that a pair of cascaded r-CBGs can resolve and then recombine the spectrum.

Non-differentiable angular dispersion as an optical resource.

Introducing angular dispersion into a pulsed field associates each frequency with a particular angle with respect to the propagation axis. A perennial yet implicit assumption is that the propagation angle is differentiable with respect to the frequency. Recent work on space-time wave packets has shown that the existence of a frequency at which the derivative of the propagation angle does not exist-which we refer to as non-differentiable angular dispersion-allows for the optical field to exhibit unique and useful characteristics that are unattainable by endowing optical fields with conventional angular dispersion.

Reversible inter-degree-of-freedom optical-coherence conversion via entropy swapping.

The entropy associated with an optical field quantifies the field fluctuations and thus its coherence. Any binary optical degree-of-freedom (DoF) - such as polarization or the field at a pair of points in space - can each carry up to one bit of entropy. We demonstrate here that entropy can be reversibly swapped between different DoFs, such that coherence is converted back and forth between them without loss of energy.

Excitation of surface plasmon polaritons by diffraction-free and vector beams.

Surface plasmon polaritons (SPPs) are traditionally excited by plane waves within the Rayleigh range of a focused transverse-magnetic (TM) Gaussian beam. Here we investigate and confirm the coupling between SPPs and two-dimensional Gaussian and Bessel-Gauss wave packets, as well as one-dimensional light sheets and space-time wave packets. We encode the incoming wavefronts with spatially varying states of polarization; then we couple the respective TM components of radial and azimuthal vector beam profiles to confirm polarization-correlation and spatial-mode selectivity.

Synthesis of near-diffraction-free orbital-angular-momentum space-time wave packets having a controllable group velocity using a frequency comb.

Novel forms of light beams carrying orbital angular momentum (OAM) have recently gained interest, especially due to some of their intriguing propagation features. Here, we experimentally demonstrate the generation of near-diffraction-free two-dimensional (2D) space-time (ST) OAM wave packets (ℓ = +1, +2, or +3) with variable group velocities in free space by coherently combining multiple frequency comb lines, each carrying a unique Bessel mode. Introducing a controllable specific correlation between temporal frequencies and spatial frequencies of these Bessel modes, we experimentally generate and detect near-diffraction-free OAM wave packets with high mode purities (>86%).

Space-time wave packets localized in all dimensions.

Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to nonlinear and quantum optics. However, synthesizing such wave packets requires introducing non-differentiable angular dispersion with high spectral precision in two transverse dimensions, a capability that has eluded optics to date. Here, we describe an experimental strategy capable of sculpting the spatio-temporal spectrum of a generic pulsed beam by introducing arbitrary radial chirp via two-dimensional conformal coordinate transformations of the spectrally resolved field.

Spatial resolution of omni-resonant imaging.

Omni-resonance refers to the broadening of the spectral transmission through a planar cavity, not by changing the cavity structure, but by preconditioning the incident optical field. As such, broadband imaging can be performed through such a cavity with all the wavelengths simultaneously resonating. We examine here the spatial resolution of omni-resonant imaging and find that the spectral linewidth of the cavity resonance determines the spatial resolution.

Refraction of space-time wave packets in a dispersive medium.

Space-time (ST) wave packets are a class of pulsed optical beams whose spatiotemporal spectral structure results in propagation invariance, tunable group velocity, and anomalous refractive phenomena. Here, we investigate the refraction of ST wave packets normally incident onto a planar interface between two dispersive, homogeneous, isotropic media. We formulate a new, to the best of our knowledge, refractive invariant for ST wave packets in this configuration, from which we obtain a law of refraction that determines the change in their group velocity across the interface.

Consequences of non-differentiable angular dispersion in optics: tilted pulse fronts versus space-time wave packets.

Conventional diffractive and dispersive devices introduce angular dispersion (AD) into pulsed optical fields, thus producing so-called 'tilted pulse fronts'. Naturally, it is always assumed that the functional form of the wavelength-dependent propagation angle[s] associated with AD is differentiable with respect to wavelength. Recent developments in the study of space-time wave packets - pulsed beams in which the spatial and temporal degrees of freedom are inextricably intertwined - have pointed to the existence of non-differentiable AD: field configurations in which the propagation angle does not possess a derivative at some wavelength.

Arbitrarily accelerating space-time wave packets.

All known realizations of optical wave packets that accelerate along their propagation axis, such as Airy wave packets in dispersive media or wave-front-modulated X-waves, exhibit a constant acceleration; that is, the group velocity varies linearly with propagation. Here we synthesize space-time wave packets that travel in free space with arbitrary axial acceleration profiles, including group velocities that change with integer or fractional exponents of the distance. Furthermore, we realize a composite acceleration profile: the wave packet accelerates from an initial to a terminal group velocity, before decelerating back to the initial value.

Space-time vector light sheets.

We introduce the space-time (ST) vector light sheet. This unique one-dimensional ST wave packet is characterized by classical entanglement (CE), a correlation between at least two non-separable intrinsic degrees-of-freedom (DoFs), which in this case are the spatiotemporal DoFs in parallel with the spatial-polarization DoFs. We experimentally confirm that the ST vector light sheet maintains the intrinsic features of the uniformly polarized ST light sheet, such as near-diffraction-free propagation and self-healing, while also maintaining the intrinsic polarization structure of common vector beams, such as those that are radially polarized and azimuthally polarized.

Realizing normal group-velocity dispersion in free space via angular dispersion.

It has long been thought that normal group-velocity dispersion (GVD) cannot be produced in free space via angular dispersion. Indeed, conventional diffractive or dispersive components such as gratings or prisms produce only anomalous GVD. We identify the conditions that must be fulfilled by the angular dispersion introduced into a plane-wave pulse to yield normal GVD.

Refraction of space-time wave packets: III. experiments at oblique incidence.

The refraction of space-time (ST) wave packets at planar interfaces between non-dispersive, homogeneous, isotropic dielectrics exhibits fascinating phenomena, even at normal incidence. Examples of such refractive phenomena include group-velocity invariance across the interface, anomalous refraction, and group-velocity inversion. Crucial differences emerge at oblique incidence with respect to the results established at normal incidence.

Refraction of space-time wave packets: II. experiments at normal incidence.

The refraction of space-time (ST) wave packets offers many fascinating surprises with respect to conventional pulsed beams. In the first paper in this sequence [J. Opt.

Refraction of space-time wave packets: I. theoretical principles.

Space-time (ST) wave packets are pulsed optical beams endowed with precise spatio-temporal structure by virtue of which they exhibit unique and useful characteristics such as propagation invariance and tunable group velocity. We study in detail here, and in two accompanying papers, the refraction of ST wave packets at planar interfaces between non-dispersive, homogeneous, and isotropic dielectrics. We formulate a law of refraction that determines the change in the ST wave-packet group velocity across such an interface as a consequence of a newly identified optical refractive invariant that we call the "spectral curvature".

Temporal Talbot effect in free space.

The temporal Talbot effect refers to the periodic revivals of a pulse train propagating in a dispersive medium and is a temporal analog of the spatial Talbot effect with group-velocity dispersion in time replacing diffraction in space. Because of typically large temporal Talbot lengths, this effect has been observed to date in only single-mode fibers, rather than with freely propagating fields in bulk dispersive media. Here we demonstrate for the first time, to the best of our knowledge, the temporal Talbot effect in free space by employing dispersive space-time wave packets, whose spatiotemporal structure induces group-velocity dispersion of controllable magnitude and sign in free space.

Isochronous space-time wave packets.

The group delay incurred by an optical wave packet depends on its path length. Therefore, when a wave packet is obliquely incident on a planar homogeneous slab, the group delay upon traversing it inevitably increases with the angle of incidence. Here, we confirm the existence of isochronous "space-time" (ST) wave packets: pulsed beams whose spatiotemporal structure enables them to traverse the layer with a fixed group delay over a wide span of incident angles.

Space-time wave packets violate the universal relationship between angular dispersion and pulse-front tilt.

Introducing angular dispersion into a pulsed field tilts the pulse front with respect to the phase front. There exists between the angular dispersion and pulse-front tilt a universal relationship that is device-independent, and also independent of the pulse shape and bandwidth. We show here that this relationship is violated by propagation-invariant space-time (ST) wave packets, which are pulsed beams endowed with precise spatiotemporal structure corresponding to a particular form of angular dispersion.